Elasticity, an often-overseen parameter in the development of nanoscale drug delivery systems

• Agnes-Valencia Weiss and
• Marc Schneider

Beilstein J. Nanotechnol. 2023, 14, 1149–1156, doi:10.3762/bjnano.14.95

• determined by the Young’s modulus, bulk modulus or shear modulus, viscoelastic properties or deformability) as well as the measurement method to quantify these properties. Anselmo et al. as well as Nie et al. gave comprehensive overviews and definitions of different measurements of mechanical properties [16

Transferability of interatomic potentials for silicene

• Marcin Maździarz

Beilstein J. Nanotechnol. 2023, 14, 574–585, doi:10.3762/bjnano.14.48

• quantify the potentials under examination. For 2D materials, directional 2D Young’s moduli, 2D Poisson’s ratios, and the 2D shear modulus, are often used instead of elastic constants Cij. Because of the symmetry of hexagonal lattices, these reduce to one 2D Young’s modulus E and one 2D Poisson’s ratio ν

Quantitative dynamic force microscopy with inclined tip oscillation

• Philipp Rahe,
• Daniel Heile,
• Reinhard Olbrich and
• Michael Reichling

Beilstein J. Nanotechnol. 2022, 13, 610–619, doi:10.3762/bjnano.13.53

• for the investigation of in-plane material properties, such as the in-plane shear modulus [16]. Last, the influence of the inclination between oscillation direction and surface plane has been used in lateral force microscopy to determine the probe oscillation amplitude [17]. Here, we extend the

Theoretical understanding of electronic and mechanical properties of 1T′ transition metal dichalcogenide crystals

• Seyedeh Alieh Kazemi,
• Sadegh Imani Yengejeh,
• Vei Wang,
• William Wen and
• Yun Wang

Beilstein J. Nanotechnol. 2022, 13, 160–171, doi:10.3762/bjnano.13.11

• ′ polytype; anisotropy; density functional theory; layered transition metal dichalcogenide crystals; shear modulus; Young’s modulus; Introduction Layered transition metal dichalcogenides (TMDs) have received increasing attention as important and versatile materials for new applications in different sectors

• ability to predict the mechanical characteristics of 1T′ TMD materials [33]. In this comparative study, the electronic and mechanical properties including shear modulus (G), bulk modulus (B), Young’s modulus (Y), Poisson’s ratio (ν), and microhardness (H), of MoS2, MoSe2, WS2, and WSe2 crystals with the

• of Voigt bulk modulus (BV), Reuss bulk modulus (BR), Voigt shear modulus (GV), and Reuss shear modulus (GR) in this study are calculated as [46]: where Sij is the compliance tensor and Sij = Cij−1; Cij are the elastic constants. Voigt and Reuss values provide the theoretical upper- and lower-bound on

Effects of temperature and repeat layer spacing on mechanical properties of graphene/polycrystalline copper nanolaminated composites under shear loading

• Chia-Wei Huang,
• Man-Ping Chang and
• Te-Hua Fang

Beilstein J. Nanotechnol. 2021, 12, 863–877, doi:10.3762/bjnano.12.65

• ) composites under shear loading are investigated by molecular dynamics simulations. The effects of different temperatures, graphene chirality, repeat layer spacing, and grain size on the mechanical properties, such as failure mechanism, dislocation, and shear modulus, are observed. The results indicate that

• -healing occurs in the armchair direction, which causes the shear stress to increase after failure. Furthermore, the maximum shear stress and the shear strength of the composites decrease with an increase of the repeat layer spacing. Also, the shear modulus increases by increasing the grain size of copper

• the composites. Figure 4 shows the shear modulus of GPCuNL composites at different temperatures and with different graphene chiralities. With the increase of temperature, the shear modulus of the zigzag and armchair GPCuNL composites significantly decreased. Moreover, the reduction rate of the shear

Spontaneous shape transition of Mn_xGe_1−x islands to long nanowires

• S. Javad Rezvani,
• Luc Favre,
• Gabriele Giuli,
• Yiming Wubulikasimu,
• Isabelle Berbezier,
• Augusto Marcelli,
• Luca Boarino and
• Nicola Pinto

Beilstein J. Nanotechnol. 2021, 12, 366–374, doi:10.3762/bjnano.12.30

• plane, the Poisson ratio, and the shear modulus of the substrate, respectively [34]. The value of Γ/ch controls the final distribution and size of the islands. In particular, if Γ/ch ≫ 1, then α0 becomes too large to reduce the edge-to-area ratio. While the mechanism described here applies to the

Determination of elastic moduli of elastic–plastic microspherical materials using nanoindentation simulation without mechanical polishing

• Hongzhou Li and
• Jialian Chen

Beilstein J. Nanotechnol. 2021, 12, 213–221, doi:10.3762/bjnano.12.17

• of an elastic half space by a flat, cylindrical punch leads to a simple relation between P and h of the form [27] where a is the radius of the cylinder and G is the shear modulus. Noting that the contact area (i.e., the projected area or cross-sectional area of elastic contact) A is equal to πa2 and

• that the shear modulus is equal to E/[2(1 + ν)], differentiating P with respect to h leads to where S = dP/dh is the initial stiffness of the unloading curve, defined as the slope of the upper portion of the unloading curve during the initial stages of unloading (also called contact stiffness), and E

Design of V-shaped cantilevers for enhanced multifrequency AFM measurements

• Mehrnoosh Damircheli and
• Babak Eslami

Beilstein J. Nanotechnol. 2020, 11, 1525–1541, doi:10.3762/bjnano.11.135

• , y(x,t), ϕ(x,t), ρ, I, E and c are shear coefficient, shear modulus, area of cross section, transverse deflection of the beam, bending angle of the beam, mass density of the beam, moment of inertia of cross section, Young’s modulus, and internal damping of the cantilevers, respectively. The cross

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

• Enrique A. López-Guerra and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 1409–1418, doi:10.3762/bjnano.11.125

• viscoelastic harmonic functions as a function of frequency in the range of frequencies involved in the experiment. For example, for the Generalized Maxwell model, which this paper focuses on, the storage shear modulus, G′, which accounts for the elastic behavior of the material under harmonic excitation, is

• given by [15]: where ω is the angular frequency, equal to 2πν. At zero frequency, G′, is equal to Ge, the rubbery shear modulus, and as the frequency increases, it converges to the glassy shear modulus, Gg, which is given by: The loss shear modulus, G″, which accounts for the viscous behavior of the

• material, is given by [15]: where G″(ω) at both zero and infinitely large frequencies converges to zero, implying pure elastic behavior at those extrema. Note that the above equations and paragraphs refer to shear moduli (e.g., storage shear modulus and loss shear modulus) instead of tensile (Young´s

Nonclassical dynamic modeling of nano/microparticles during nanomanipulation processes

• Moharam Habibnejad Korayem,
• Ali Asghar Farid and
• Rouzbeh Nouhi Hefzabad

Beilstein J. Nanotechnol. 2020, 11, 147–166, doi:10.3762/bjnano.11.13

• χij are the symmetric part of couple stress and curvature tensors, respectively. Also, the relation for couple stress and curvature tensors is written as [27] where l is the material length scale parameter for considering the size effects, and G is the shear modulus. The displacement fields for the

Mechanical and thermodynamic properties of Aβ₄₂, Aβ₄₀, and α-synuclein fibrils: a coarse-grained method to complement experimental studies

• Adolfo B. Poma,
• Horacio V. Guzman,
• Mai Suan Li and
• Panagiotis E. Theodorakis

Beilstein J. Nanotechnol. 2019, 10, 500–513, doi:10.3762/bjnano.10.51

• the requirement of a different experimental setup, namely, the more involved sonification method [34]. Moreover, the experimental calculation of the shear modulus (S) can be realised by suspending the fibril between two beams and pressing the free part against the indenter, which gives rise to the

• before for the determination of YL are not applicable for the calculation of the shear modulus (S) at the nanoscale. Hence, an improved version of the single three-point bending technique was developed for the calculation of S [55]. It combines a movement along the z-axis (perpendicular to the main

• of shear modulus (S) computed for vpull = 0.0005 Å/τ are listed in Table 2. In our studies, these values show a large dependence on the type of Aβ fibril. We find that S for Aβ42 is about 1.6 GPa, while for Aβ40 it is equal to 0.7 GPA. The 2.3-fold increase supports the picture that the Aβ42 fibril

Pull-off and friction forces of micropatterned elastomers on soft substrates: the effects of pattern length scale and stiffness

• Peter van Assenbergh,
• Marike Fokker,
• Julian Langowski,
• Jan van Esch,
• Marleen Kamperman and
• Dimitra Dodou

Beilstein J. Nanotechnol. 2019, 10, 79–94, doi:10.3762/bjnano.10.8

• are present is referred to as the elastocapillary length l, which is defined as l = γ/μ, where γ is the surface tension of the substrate and μ is the elastic shear modulus of the substrate [26]. If the length scale of the microscale features is in the order of the elastocapillary length, indentation

• PVA-18, respectively. The elastocapillary length of PVA (defined as l = γPVA/μPVA [26], with surface tension γPVA ≈ 50 kPa [32] and elastic shear modulus μPVA ≈ 12 kPa for PVA-12) is in the order of 400 nm. Similarly, the elastocapillary length of PVA-18 is in the order of 300 nm. Pull-off forces of

Evidence of friction reduction in laterally graded materials

• Roberto Guarino,
• Gianluca Costagliola,
• Federico Bosia and
• Nicola Maria Pugno

Beilstein J. Nanotechnol. 2018, 9, 2443–2456, doi:10.3762/bjnano.9.229

• time evolution obtained with FEM is also shown. In this case, the behaviour is strongly dependent on the thickness of the block. The time interval Δts needed to reach the static friction peak can be estimated starting from the shear stress τ = Gγ, where G is the shear modulus. If the shear deformation

Electrospun one-dimensional nanostructures: a new horizon for gas sensing materials

• Muhammad Imran,
• Nunzio Motta and
• Mahnaz Shafiei

Beilstein J. Nanotechnol. 2018, 9, 2128–2170, doi:10.3762/bjnano.9.202

Nanoprofilometry study of focal conic domain structures in a liquid crystalline free surface

• Anna N. Bagdinova,
• Evgeny I. Demikhov,
• Nataliya G. Borisenko and
• Sergei M. Tolokonnikov

Beilstein J. Nanotechnol. 2017, 8, 2544–2551, doi:10.3762/bjnano.8.254

• the elastic moduli of liquid crystals. The shear modulus, G, is given as where C and C1 are scaling constants depending on surfactant, t is the relative temperature, γ is the surface tension coefficient of the free surface with FCDs, and L is the FCD dimension. This relation underlines that the

• smectic-A phase with FCDs has different elastic properties compared to an ideal smectic-A sample. Usually, it is observed that for the shear parallel to the smectic layers, the shear modulus is zero. In the case of a SmA sample with a FCD, the free sliding is hindered by the presence of FCDs. This problem

A comparative study of the nanoscale and macroscale tribological attributes of alumina and stainless steel surfaces immersed in aqueous suspensions of positively or negatively charged nanodiamonds

• Colin K. Curtis,
• Antonin Marek,
• Alex I. Smirnov and
• Jacqueline Krim

Beilstein J. Nanotechnol. 2017, 8, 2045–2059, doi:10.3762/bjnano.8.205

• of the liquid under no-slip boundary conditions are given by [35]: where ρq = 2.648 g/cm3 is the density and µq = 2.947 × 1011 g/cm/s2 is the shear modulus of quartz. Immersion of one side of a 5 MHz resonant frequency QCM in water at room temperature (ρ3 = 1 g/cm3, η3 = 0.01 poise) results in a δf

Stick–slip boundary friction mode as a second-order phase transition with an inhomogeneous distribution of elastic stress in the contact area

• Iakov A. Lyashenko,
• Vadym N. Borysiuk and
• Valentin L. Popov

Beilstein J. Nanotechnol. 2017, 8, 1889–1896, doi:10.3762/bjnano.8.189

• written in the form: where we have introduced the shear modulus of the lubricant μ, that takes nonzero values only in solid-like states. The stationary values of the order parameter φ0 can be estimated from the condition ∂f / ∂φ = 0 in the following form: According to Equation 3, the stationary value of

• the order parameter φ0 decreases with the growth of both temperature T and elastic strain εel. When the strain exceeds a critical value stationary values of the order parameter φ0 and shear modulus μ0 (according to Equation 2) equal to zero and the lubricant melts. In the case εel < εel,c as defined

• half-space characterized by an effective shear modulus [24] Assuming that the upper stamp has mass m, and the coordinate of the stamp center is X, let us consider the situation where the stamp is driven by a spring with the constant stiffness K. The free end of the spring moves with a constant velocity

Deformation-driven catalysis of nanocrystallization in amorphous Al alloys

• Rainer J. Hebert,
• John H. Perepezko,
• Harald Rösner and
• Gerhard Wilde

Beilstein J. Nanotechnol. 2016, 7, 1428–1433, doi:10.3762/bjnano.7.134

• less than 10 nm, but the origin of the deformation-driven nanocrystallization remains an area of active research. Intense deformation in metallic glasses occurs in shear bands at stress levels of more than about 30% of the shear modulus and at temperatures of below approximately 0.7·Tg [36]. If intense

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

• Mostafa Mirzaei and
• Yaser Kiani

Beilstein J. Nanotechnol. 2016, 7, 511–523, doi:10.3762/bjnano.7.45

• approach may be modified with the introduction of the efficiency parameters. Under such modification, Young’s modulus and the shear modulus of the composite media take the form: In this formula, the properties of the CNT are denoted by a superscript CN and that those belong to matrix are denoted by a

• superscript m. Following the classical solid mechanics notation, E and G are the elastic modulus and shear modulus of the constituents, respectively. In comparison to the conventional rule of mixtures approach, three unknown constants, η1, η2 and η3, are introduced in Equation 1; these are known as efficiency

• is free of CNTs and the top has the maximum volume fraction of CNTs. Unlike these three types, in the UD case, each surface of the plate has the same volume fraction of CNTs. Similar to the shear modulus and Young’s modulus, Poisson’s ratio and the mass density of the composite media may be written

Active multi-point microrheology of cytoskeletal networks

• Tobias Paust,
• Tobias Neckernuss,
• Lina Katinka Mertens,
• Ines Martin,
• Michael Beil,
• Paul Walther,
• Thomas Schimmel and
• Othmar Marti

Beilstein J. Nanotechnol. 2016, 7, 484–491, doi:10.3762/bjnano.7.42

• ; Introduction The dynamic shear modulus describes properties of polymer networks. It can be determined by recording and mathematically transforming the thermal motion of a particle embedded in a viscoelastic medium into the frequency domain. Since no external forces are applied to the motion of the particle

• , this method is named passive microrheology [1][2][3][4]. The resulting shear modulus shows the elastic and diffusive behavior of the investigated medium over the frequency range accessible by the measuring setup. This output is the result of different methods handling the unilateral Laplace transform

• [5][6][7]. By exciting a particle with an oscillating force, the shear modulus at a specific frequency can be determined by measuring the response of the particle. The motion of the particle also includes information about the damping and the viscosity of the surrounding medium. This method is known

Fabrication and characterization of novel multilayered structures by stereocomplexion of poly(D-lactic acid)/poly(L-lactic acid) and self-assembly of polyelectrolytes

• Elena Dellacasa,
• Li Zhao,
• Gesheng Yang,
• Laura Pastorino and
• Gleb B. Sukhorukov

Beilstein J. Nanotechnol. 2016, 7, 81–90, doi:10.3762/bjnano.7.10

• resonance frequency of the quartz crystal oscillator, A is the area of the electrode (0.205 cm2), ρq is the quartz density (2.648 g/cm3), and µq is its shear modulus (2.947·1011 g/cm·s2). The cleaned electrodes were immersed into aqueous solutions of PSS and PAH (2 mg/mL) for 15 min and PLL (5 mg/mL) for 30

Lower nanometer-scale size limit for the deformation of a metallic glass by shear transformations revealed by quantitative AFM indentation

• Arnaud Caron and
• Roland Bennewitz

Beilstein J. Nanotechnol. 2015, 6, 1721–1732, doi:10.3762/bjnano.6.176

• the limit of infinite depth and δ* is a characteristic length depending on the indenter geometry, the shear modulus, the Burgers vector, and H0. For metallic glasses an indentation size effect has also been observed and has been discussed on the basis of accumulation of STZs during indentation and

Electrical characterization of single molecule and Langmuir–Blodgett monomolecular films of a pyridine-terminated oligo(phenylene-ethynylene) derivative

• Henrry M. Osorio,
• Santiago Martín,
• María Carmen López,
• Santiago Marqués-González,
• Simon J. Higgins,
• Richard J. Nichols,
• Paul J. Low and
• Pilar Cea

Beilstein J. Nanotechnol. 2015, 6, 1145–1157, doi:10.3762/bjnano.6.116

• 5 MHz, Δm(g) is the mass change, A is the electrode area, ρq is the density of the quartz (2.65 g·cm-3), μq is the shear modulus (2.95 × 1011 dyn·cm−2), and the molecular weight of 1 is 280 g·mol−1. Thus, the surface coverage of 1 incorporated into LB films, obtained from Equation 1, is 0.98 × 10−9

Stiffness of sphere–plate contacts at MHz frequencies: dependence on normal load, oscillation amplitude, and ambient medium

• Jana Vlachová,
• Rebekka König and
• Diethelm Johannsmann

Beilstein J. Nanotechnol. 2015, 6, 845–856, doi:10.3762/bjnano.6.87

• contact stiffness, κ, by Equation 2. G* is the effective modulus, given as G and v are the shear modulus and the Poisson ratio, respectively. The indices 1 and 2 label the contacting media. Given that the contact diameter can be estimated to be larger than 1 µm, we ignore the thin films present (SiO2

• , PMMA, gold) and use the same values on both sides. For the sake of quantitative modeling (see Figure 5 below) we keep the Poisson number fixed at v1 = v2 = 0.17 and express the shear modulus as where E is the Young’s modulus and E is a fit parameter. The contact radius, a, is assumed to obey the JKR

On the structure of grain/interphase boundaries and interfaces

• K. Anantha Padmanabhan and
• Herbert Gleiter

Beilstein J. Nanotechnol. 2014, 5, 1603–1615, doi:10.3762/bjnano.5.172

• summarized in [53][54][55][56][57][60][61][62]. The shear modulus and the free volume present in the basic sliding unit, γ0, (composition, impurity/solute/dopant content dependent) can be determined by using ab initio calculations, in particular the tight binding model, which is computationally less

• narrow, while the one associated with the boundaries is so broad that it appears almost like a uniform background, i.e., there are wide fluctuations in the structures of the boundaries. This difference is traced to the fact that a glass has shear modulus that tends to zero as time tends to infinity. In